Solid propellant grain

ABSTRACT

A solid propellant grain including a binder matrix containing circumferentially disposed, elongated, hollow strands of filaments filled with reactive combustible material.

United States Patent [56] References Cited UNIT ED STATES PATENTS 2,072,671 3/1937 Foulke 102/40 3,056,701 10/ 1962 Fritzler 102/98 3,105,350 10/ 1963 Eichenberger 102/98 X 3,129,561 4/1964 Priapi 102198 X 3,140,659 7/1964 Van Antodalen et a] 102/98 X 3,140,663 7/1964 Rumbel et a1 102/19 X 3,143,446 8/1964 Berman 149/19 X 3,159,104 12/1964 l-lodgson 102/98 3,204,560 9/ 1965 Gustavson 102/98 Primary ExaminerSamue1 W. Engle Attorneys-William R. Lane, Thomas S. MacDonald and Stuart W. Wohlgemuth ABSTRACT: A solid propellant grain including a binder matrix containing circumferentially disposed, elongated, hollow strands of filaments filled with reactive combustible material.

2 f as PATENTEDnm 19 l97l SHEET 1 CF 2 INVENTORS SYLVESTER C. BRITTON y FRANCIS A. WARREN ATTORNEY PATENTEnum 19 l97| SHEET 2 BF 2 INVENTORS SYLVESTER C. BRITTON BY FRANCIS A. WARREN A RNEY SOLID PROPELLANT GRAIN This invention relates to solid propellant grain configurations; More particularly, the invention pertains to solid propellant grains having highly reactive materials therein and in a method of makingsame. .Solid propellant grains of the composite type are ordinarily composed of an organic polymeric binder,-a particulate fuel and a particulate oxidizer dispersed within the binder.

The need for a significant increase in the performance of solid propellants of this type is well recognized. Promising combinations of fuel and oxidizer have resulted from chemical synthesis studies sponsored by various sources. A number of interesting ingredients with the potential of improving solid propellant performance have been unveiled. Few such propellants incorporating such combinations have been realized. Almost all suggested combinations of potentially more energetic compounds require a degree of reactivity on the part of one or more of the ingredients which precludes processing by any of the methods commonly used today. Initially, the more energetic compounds present other problems as will be described.

The incorporation of materials such as nitronium perchlorate in the conventional matrices found today result in a class 9 propellant, in other words, a propellant results that has the sensitivity of such explosives as nitroglycerin, being extremely hazardous to handle and impractical because of this danger. The problem has application to propellant ingredients such as the hydrazine nitroforrn, and -NF, compounds. The problem also pertains to the utilization of various high-energy oxidizers such as nitronium perchlorate which should be isolated in order to prevent the production of a class 9 propellant. Additionally, some of the energetic ingredients that may be desirous to incorporate in a grain have poor structural characteristics. The materials might be polymeric but with little strength, amorphous or in the form of pastes, gels or even liquid. As such, their incorporation in grains has been severely limited and for most practical purposes impossible.

An additional problem when using highly reactive components, even if a class 9 propellant is not produced, relates to the reactivity of the ingredients in situ. Over a period of time, undesirable chemical reactions can transpire in the grain greatly affecting its ultimate performance. Additionally, of course, some of the possible constituents could react spontaneously preventing the fabrication of a grain.

Because of the above problems, various techniques have been attempted all directed to encapsulation of the active particle of material. Among such techniques are phase-separation methods, a nozzle process, dipping, vapor deposition an electrolytic plating. More elaborate and classic processes involve sealing the reactive material into minute containers of aluminum or other appropriate material into minute containers of aluminum or other appropriate material by crimping plastic sealing, and ultrasonic welding. All of these methods give rise to new problems in the processing of propellants. Among some of the problems is the difficulty of forming a continuous, reliable, impervious film around each active particle. There is also the probable puncturing or rupturing of the capsule during normal solid propellant mixing, in forming applications, as well as during mandrel removal and grain trimming. Further problems result in trying to prevent agglomeration after encapsulation and in effecting adequate inspection for complete protection. These processes are further limited as to the capsule material which may be used as set by the encapsulation process, the characteristics of the reactive material, and the ability of the coating to adhere to the remainder of the propellant in the cured state.

It is an object of this invention to provide a solid propellant grain having high impulse.

A further object of this invention is to provide solid propellant grains shaving very highly reactive components.

A still further object of this invention is to provide a method for producing solid propellant grains having highly reactive components therein.

One other object of the invention is to provide a means for utilizing high-energy components having poor inherent struc- The above and other objects of the invention become apparent from the following detailed description. To meet the problems stated, a unique solid propellant and method of I making it' has been devised. Specifically, the method comprises the formation of strands or filaments of material filled with the reactive, high-energy components and the use of these elements in binder matrix to from the solid propellant grains. The walls of the filaments protect the reactants from other ingredients which form part of the propellant composition. Within the filaments or strands may be situated either highly reactive or particulate oxidizer or the highly reactive particulate fuels or a mixture of both. The filaments or strands are considered to have essentially infinite length compared to their cross-sectional dimension.

The invention will be explained in more detail in the following description with reference to the drawings in which:

FIG. 1 is a pictorial representation of a filled filament of the invention;

FIG. 2 is a pictorial view of a typical method for fabricating a strand or filament filled with a highly reactive material,

FIG. 3 is a pictorial representation of a method for flattening the strand of material for ultimate use in a grain,

FIT. 4 is a pictorial representation of a method of winding a propellant grain utilizing the filaments of the invention to produce a novel grain;

FIG. 5 shows a partially sectioned perspective view illustrat ing a grain formed from the method represented by FIG. 4;

FIG. 6 shows a pictorial view of an alternative method of incorporating the filaments in the grain in a coaxial arrangement;

FIG. 7 is a partially sectioned perspective view of a grain incorporating longitudinally displaced filaments.

The basic concept of a filled filament is illustrated in FIG. I wherein the film material 9 forms a continuous coating about the filler material 10 except for the ends. By making the length of the filament large in comparison with its cross section, the exposed ends become small compared to the total length of the material. For complete protection the ends would be sealed.

As shown in FIG. 2, the filament element 11 is comprised of a ribbon 13 which may be made of a material such as polyethylene. The polyethylene ribbon is bent up at the edges to form a trough. The ribbon passes under a feeder or any type of similar mechanism which deposits a metered quantity of the reactive material 15 which by way of example will be referred to as All-i, in the trough formed. The edges I7 of the ribbon are brought together and sealed by means of a sealer 19 which can apply heat thereto forming a continuous tube or filament. As seen in FIG. 3, the tube 11 can be rolled flat between the pair of rollers 21 to the final tape form and stored on the reel 23 to maintain distribution of the powder within the tube cavity. Polyethylene is one of an example of the materials for forming the casing of the tube or filament because of its chemical inertness, easy scalability with very little heat, and high-quality fuel content. Other material than polyethylene can be used when fiat tape is desired. By the process described for forming the tube, it is not necessary to make a heat seal in close proximity to AlH because the material does not fill the cavity until the tube is rolled fiat. However, if heat is a problem, suitable adhesives compatible with AIH, can be used. The All-I as noted, is in the form of crystalline particles of 20-100 microns in diameter.

One method for making the propellant grain is to unwind the filament from a storage wheel and rewind it on a propellant core which is held and rotated by a winding machine. As disclosed in FIG. 4, a tape II would be directed to a mandrel 24. Before reaching the mandrel, the tape is coated with a matrix of a binder and oxidizer 26 which is deposited from a feeder 28. The action is similar to the deposit of toothpaste from a tube. As the matrix-loaded tape is spirally wound on the core of mandrel 24, a pressure roller 31 distributes and consolidates the matrix. In the manufacture of the grain it is of course necessary that both ends of the filled filament be sealed in essentially the same manner that the sealing transpired in the FIG. 2 around the tube that was sealed along its length. FIG. 5 depicts the final grain with the filled filaments ll helically wound about the center axis. The matrix material 26 serves to bind the filaments together upon curing. It should be apparent that several tapes may be fed to the grain at once in a manner similar to that found in conventional filament windmg.

An alternative embodiment of the invention disclosed in FIG. 6 and FIG. 7 wherein the grains of this invention can be constructed by conventional casting molds and the matrix is cast around them to fill the voids. In the example shown in FIG. 5, an outer case or mold wall 33 is shown in which the propellant can be cast. Spacer plated 35 are disposed adjacent and within each end of the cylindrically shaped case 33. The spacer plates serve to preserve the geometrical arrangement of the filled filaments 11 within the grain. A plurality of apertures 37 are provided in the spacer plates through which the matrix utilized can be admitted between the filaments to form the propellant grain when the area 39 between the two spacer plates is entirely filled with the matrix, the spacer plates may then be cut away and the remainder of the casing filled with the matrix. The filaments will maintain their position in the matrix once the area between the space plates is filled up due to viscosity of the matrix. After the entire casing 33 is filled, it can then be cured in the normal procedure and is ready for use as a propellant. The final product is shown in FIG. 7 wherein the filled filament 11 are disposed longitudinally within the grain parallel to the center axis of the grain.

The main requisites for the encapsulating filament are that it be inert relative to the material encapsulated within it, that it be capable of bonding to the matrix and that it be readily sealable. Examples include most of the plastic films such as polyehtylenes, Mylar types, polybutadienes, polystyrenes, butadienes, isoprene, vinyl, polyvinylchloride, acrylics, polyesters, polypropylene, polyamides and the like. Any compatible metal can be used including aluminum, tin and the like. Additionally, materials such as cloth and paper could be used.

Though the invention has peculiar applicability to highly energetic materials as previously described, it also offers unique advantages to producing conventional grains. In large cast grains the quantities of hazardous materials handled prior to the final fabrication are usually large. That is, large batches are mixed, cast and cured, all in potentially hazardous operations. This hazard is greatly minimized in this invention since the fuel and oxidizer can be compounded separately and are never actually intimately mixed prior to combustion. Thus, metal fuels in the propellant grain of this invention preferably contain predominantly one or more of the metals of groups l-A, Il-A, Ill-A, and groups I-B through VII-B, and group VIII of the periodic table. Thus, the metal may contain group l-A elements such as lithium, group ll-A metals is aluminum. The metals of Group [-3 through VII-B include copper, silver, zinc, cadmium, titanium, zirconium, vanadium, niobium, chromium, molybdenum, tungsten, manganese, iron, cobalt, nickel, ruthenium, rhodium, osmium palladium, and platinum. Additionally, hydrides of the metals, such as beryllium hydride and aluminum hydride are contemplated.

The oxidizable polymeric material employed in the preparation of the reinforced compositions of this invention can be any organic polymer whether naturally occuring or synthetically prepared. Thus, thermoplastic, thermosetting, elastomeric, polymeric, and plastic materials of any description may be employed. These material may be either naturally occurring, modified materials occurring in nature, or synthetically prepared.

Among the thermoplastic materials which may be employed as binders are polymers and copolymers of monoolefinic hydrocarbons having at least two carbon atoms. Thus, the polymers and the copolymers of ethylene, propylene, various butenes, pentenes, and hexenes, as well as the halogenated counterparts of these olefins may be employed in the practice of this invention. Among the thermosetting polymeric materials which may be employed are those plastics and resins which cure to a solid upon the application of heat with or without a chemical curing agent. Illustrative examples of this class of material include the polyurethane resins, epoxide resins, polyester materials, and di-(thioalkoxy) methylene polymers (polysulfide polymers). In addition, elastomers, such as the natural and synthetic rubbers, may be practicably and profitably employed in the practice of this invention. The synthetic rubbers are ordinary polymers and copolymers of a diolefin (as a major constituent) with other olefin constituents and which are subject to curing with a crosslinking agent such as MAPO, which is tris l-(2-methyl)-aziridinyl phosphine oxide. In addition to the above, organic polymers derived from naturally occurring nonelastomeric polymeric materials may be employed in the practice of this invention.

In general carbohydrate condensation-type polymers, amino acid condensation polymers, synthetic linear condensation polymers such as hydrocarbon and vinyl-type polymers, and cross-linking polymers may be employed to prepare the binders of this invention.

The condensation-type polymers are cellulose, cellulose nitrate, cellulose acetate, cellulose acetate-butyrate, ethylcellulose, and the cellulose ethers such as methyl carboxymethyl, hydroxyethyl, cyanoethyl and benzyl cellulose.

Examples of the amino acid condensation polymers are regenerated proteins such as casein and vegetable globulins. Synthetic linear condensation polymers which may be employed in the practice of this invention include the polyamides such as nylon, and polyurethane resins, polyesters such as the alkyd and fiber-forming types, polyester and polyesteramide rubbers.

Applicable linear addition polymers include natural and vulcanized rubbers such as guttapercha, balata, and chicle, cyclized or isomerized rubber, rubber hydrochloride polybutadiene rubbers including GR-S and nitrile rubber, polychloroprene and its copolymers, polysulfide rubbers, polyisobutylene and the butyl rubbers, the various polyethylenes including chlorosulphonated polyethylene rubber, polytetrafluorethylene, polystyrene, polyvinylcarbazole and polyacenaphthylene, indene and coumarone-indene resins, polyvinyl acetate, polyvinyl alcohol, polyvinyl pyrrolidone, polyvinyl formal, polyvinyl acetal, and polyvinyl butyral.

Cross-linking polymers applicable to the present invention include cross-linking-type polyester resins, various epoxy resins, polymerized drying oils, aniline formaldehyde resins, sulphonamideformaldehyde resins, ureaformaldehyde resins, melamine-formaldehyde resins, the various phenolformaldehyde condensation resins, polysulfides, and carboxy-terminated polybutadienes.

Furthermore organic polymers containing elements other than carbon, hydrogen, oxygen, and nitrogen may be employed. For example, silicon-containing polymeric materials are advantageously adapted to the practice of this invention. The silicon-containing polymers fall into two general classes; that is, those having direct silicon-to'carbon bonds (the silanes). The silicon-containing materials of ten have a halogen in the molecule.

Among the types of nitrocellulose and nitrocellulose substitutes which may be employed are plastisols which are cellulose materials having varying degrees of nitration, fluid ball casting powder, nitroguanidine, plastisol grade nitrocellulose, l,3,bis(m-acetoguanidine)2-nitroxypropane, and histrinitroethyl nitramine.

To aid in the processing of the propellant it is often advisable to employ plasticizers in the preparation and utilization of the polymeric and plastimeric materials employed in the invention. Other plasticizers may be of the general type, inert plasticizers and explosive plasticizers. Examples of inert plasticizers include triacetin, the various phthalates such as diethyl phthalate, dibutyl phthalate, dioctyl phthalate, di(methoxyethyl) phthalate, methyl phthalyl ethyl glycolate, ethyl phthalyl ethyl glycolate and butyl phthalyl butyl glycolate, sebacates such as dibutyl and dioctyl sebacates, adipates such as dioctyl adipate and di(3,5,5-trimethylhexyl)adipate, glycol esters of higher fatty acids, organic phosphate esters such as tributoxyethyl phosphate, and the like. The explosive plasticizers include nitroglycerin, butane triol trinitrate, diglycol dinitrate, ethylene glycol dinitrate, and the like.

The solid material which may be dispersed throughout the polymer matrix is usually in finely divided form having a particle size ranging from about l-500 microns or greater in diameter. When the composition is intended as a solid propellant grain, it is often desirable to employ a combination of two or more different particle size ranges. For example, solid propellants are prepared in which the finer material comprises a'fine particle size range of from i to about 75 microns and a coarse range of from about 75 to 500. However, particles of any size within the range of [-500 microns may be employed without regard to particle size ranges may be adjusted depending upon the particular binder-fuel-oxidizer combination employed and the specific impulse desired. Tl-le solid substances with which the polymeric materials .are loaded may be inert pigments such as titanium dioxide,

lead oxide, ferric oxide, carbon black, powdered metals and alloys, metal fluorides, asbestos fibers, etc.

The solids-oxidizing agents can be compounds such as metal perchlorate and metal nitrates. The metal perchlorates employed as oxidizing agents or oxygen carriers in the compositions are anhydrous and have the general formula M(Cl0 wherein M is NH, or a metal and x is the valence of M. Since the propellant composition is required to withstand high-temperature storage, it is preferably that the melting point and the decomposition temperatures of the oxidizer be as high as possible. The perchlorate of the group lA, group [-3, and group ll-A metals are found to have the required high-temperature stability and are employed in the preparation of propellant compositions by the process of this invention. Hence, the metal perchlorates used in the preparation of the propellant compositions include lithium perchlorate, sodium perchlorate, potassium perchlorate, rubidium perchlorate, and cesium perchlorate which are the perchlorates of the metals of group l-A of the periodic table of elements; silver perchlorate which is a perchlorate of the group I-B metal; and magnesium perchlorate, calcium perchlorate, strontium perchlorate, and barium perchlorate V which are the perchlorate of the group ll-A metals. In addition to the metal perchlorates, the compound ammonium perchlorate finds extensive use in propellant compositions. The highly energetic nitronium perchlorate is also contemplated. Examples of the nitrates of the group I-A, H3 and [1-8 which are employed in preparing propellant compositions by the process of this invention are compounds such as lithium nitrate, sodium nitrate, potassium nitrate, magnesium nitrate, calcium nitrate, barium nitrate, strontium nitrate, etc. Ammonium nitrate is also used.

The ratio of total solids-to-polymeric binder material in a propellant falls in the range of from about 1:1 to above 9:1

with an optimum ratio of about 8.5:].5. In some systems the optimum ratio exists with no binder present.

Other substances which are employed in the preparation of propellants by the process of this invention include minor amounts of burning catalysts, well known in propellant compositions. These are composed of one or a mixture of two or more metal oxide powders in amounts sufficient to improve the burning rate of the composition. The amounts usually range from about 0.01 to about 3 weight percent, based on the weight of the oxidizer employed. The particle size of the powders can range from about ID to about 250 microns in diameter. Nonlimiting examples of metals that serve as burning catalysts are copper, vanadium, chromium, silver, molybdenum, zirconium, antimony, manganese, iron, cobalt, and

nickel. Examples of metal-oxide-buming catalysts are ferric oxide aluminum, copper oxide, chromic oxide, as well as 'the oxides of the other metals mentioned above.

Burning rate depressants and modifiersare, also sometimes advantageously added to the solid propellant grain of thisinvention. These are generally compounds which tend to inhibit burning reaction rates or absorb heat and; include, for example, carbonyl chloride, oximide, nitrogtia nid ine, guanidine nitrate, and oxalic acid.

Curing catalysts are often added in minor amounts to cure the polymer in the performance of the process of this invention. Nonlimiting examples of catalysts used for this purpose are aluminum chloride, tris-trimethylsilyl borate, bensoly peroxide, and other catalysts well known in the curingof plastics, resins, polymers, and rubbers. Examples of various catalysts may be found in text books such as Synthetic Rubber," by G. S. Whitley, pp. 892-933, 1954 edition, published by John Wiley and Sons, Inc., New York. The caring catalysts are added in amounts of from 0.1 to about l0 weight percent based on the weight of the polymer, resin or elastomer. The particular catalyst and amount employed depend on the state of cure desired and the nature of the polymeric material employed in the composition.

The film used to enclose the reactive material is preferably as thin as possible consistent with sufficient strength. For example, metallic film could be from ten one-thousandth to 15 one-thousandth of an inch in thickness. Plastic or polymeric films could range in thickness from thirty one-thousandth to fifty one-thousandth inch. The diameter of the filled filaments, when circular in cross section would vary depending on the size of the grain in which they are to be incorporated. For example, the diameter in average size grains could vary from one-tenth to one-twelfth inch. However, in large contemplated structures, diameters of over an inch might be utilized. It should be pointed out, that often, as shown in the drawings, the filaments are somewhat flat or oblong in the form of tapes. Other cross-sectional configurations are possible such as square or rectangular and the like. When incorporated in the propellant grains, the required amount of matrix or binder needed would vary from 5 to 30 weight percent of the grain. If the film material is essentially the same as that which comprises the propellant binder, then the above percentages would incorporate the weight of such film material.

As previously indicated, the filled filaments of the invention may contain either highly reactive oxidizers of fuels. it may be desirable, in some instances, to incorporate both fuel and oxidizer particles in separate filaments within one grain. As a result, the binder matrix would not necessarily contain either an oxidizer, or a fuel but rather would serve to bind the separate filaments containing each together in the grain. Following is a specific example of the grain made according to the described invention.

EXAMPLE I The solid propellant grain was made by casting a bindermatrix comprised of 88 percent by weight of ammonium perchlorate and 12 percent by weight of binder comprised of carboxy-terminated linear polybutadiene. MAPO (methyl aziridinyl phosphine oxide) was mixed with the binder to be used as the curative. The grain was then cured for purposes of demonstrating the invention. The shape of the grain used for the experiment was that of a cylinder 10 inches long. The outside diameter of the grain was 6 inches while the inside diameter was 4.55 inches. The cured grain of the above dimensions was prepared to receive filled tubes or filaments according to this invention. Nineteen slots, each thirteen-sixteenths of an inch wide and 4% inches long were cut in the grain parallel to the center axis in the front half of the grain. The slots were then filled with lii-inch-diameter tubes or filaments containing l5-micron aluminum powder. The filament-encapsulating material was Scotch Pack made by Minnesota Mining and Manufacturing Co.. which is a laminate of a polyester and polyethylene 2 mil. thick. The tubes were held in place by additional ammonium perchlorate-binder matrix. The slotting technique was used primarily because on an experimental basis to determine effective results, it is convenient to provide an easy way to alter distribution of fuel in the grain. Large production techniques are more closely aligned to the methods previously described. The final composition of the grain was 6.6 weight percent aluminum powder, 81.3 weight percent ammonium perchlorate, l 1.6 weight percent carboxyterminated polybutadiene binder and 0.5 weight percent of the plastic filament. The total weight of the motor was 3187 grams. The aluminum was placed toward the head end of the grain so that it would have to travel farther in the burning process before exiting from the rocket nozzle. This would insure more complete combustion of the aluminum. It is pointed out that the aluminum could easily extend the entire length of the grain, however, The throat diameter of the nozzle used in the test of this rocket was 0.995 inch. A maximum pressure developed by the motor was 1,187 p.s.i. The measured specific impulse 232.3 seconds and the burning rate was 0.338 inch per second.

EXAMPLE 2 Four-inch sections of Teflon tubing having an D or oneeighth inch, a wall thickness of 0.006 inch and a length of 4 inches were filled with a eutectic mixture consisting of 67.4 percent by weight lithium perchlorate a 32.6 percent by weight ammonium perchlorate. The ends of the tubes were sealed with Bareco Wax. Adequacy of the sealing was checked by water immersion. The tubes were then restricted on their outer surface with a synthetic rubber to prevent flashing of the flame front down the interface between tube and matrix propellant in the final grain. A baseplate for supporting and positioning the tubes one-fourth inch thick and 2.4 inch diameter was fabricated from a cured sample of conventional composite propellant containing 18 weight percent synthetic rubber binder, 66 weight percent ammonium perchlorate and 16 weight percent aluminum. Thirty-seven holes of approximately one-eighth-inch diameter were drilled into this plate at evenly spaced intervals in a hexagonal pattern.

The filled Teflon tubes were inserted into the baseplate and the assembly placed in a test motor case. The volume around the tubes was then filled with uncured propellant of the same composition as the baseplate and the final assembly cured 96 hours at 170 F.

The first of these completed test motors was fitted with a graphite nozzle of 0.173-inch throat diameter and with an igniter. Upon being ignited, the propellant grain burned to completion at a pressure between 640 and 1,220 p.s.i. A total of seven such grains was fabricated and fired. Some representative data are as follows in table 1:

EXAMPLE 3 In order to increase the burning surface of the experimental propellant charge, a slab design was developed. The slab was 4XlXa0Y inches. This slab grain was cast into a special test fixture in which the filled tubes were placed. After curing the charge was fired in a standard 2-inch test motor.

Three such grains each containing 144 tubes filled with the lithium perchlorate/ammonium perchlorate eutectic were fabricated. A control grain with no tubes was also prepared. Two of the charges contained tubes made of Teflon; the third contained aluminum tubes. When the charges were fired in 2- inch test motors all burned to completion, giving the following data as indicated in table 11.

Although the invention has been described and illustrated in detail, it is to be clearly understood that the same is by way of illustration and example only and is not to be taken by way of limitation, the spirit and scope of this invention being limited only by the terms of the appended claims.

, We claim:

propellant grain having forward and aft ends com- 2. A solid propellant grain comprising:

a binder matrix,

and enclosed elongated strands of reactive combustible material disposed in said matrix, said strands comprising hollow film filaments filled with said reactive material, said reactive material being continuous and said continuous filled filaments disposed circumferentially within said matrix. 

2. A solid propellant grain comprising: a binder matrix, and enclosed elongated strands of reactive combustible material disposed in said matrix, said strands comprising hollow film filaments filled with said reactive material, said reactive material being continuous and said continuous filled filaments disposed circumferentially within said matrix. 